The longest path in a random graph

Miklós Ajtai, János Komlós, E. Szemerédi

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

A random graph with (1+ε)n/2 edges contains a path of length cn. A random directed graph with (1+ε)n edges contains a directed path of length cn. This settles a conjecture of Erdõs.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalCombinatorica
Volume1
Issue number1
DOIs
Publication statusPublished - Mar 1981

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Longest Path
Directed graphs
Random Graphs
Path
Directed Graph

Keywords

  • AMS subject classification (1980): 05C38, 60C05, 60J80

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

The longest path in a random graph. / Ajtai, Miklós; Komlós, János; Szemerédi, E.

In: Combinatorica, Vol. 1, No. 1, 03.1981, p. 1-12.

Research output: Contribution to journalArticle

Ajtai, Miklós ; Komlós, János ; Szemerédi, E. / The longest path in a random graph. In: Combinatorica. 1981 ; Vol. 1, No. 1. pp. 1-12.
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